<html xmlns="http://www.w3.org/1999/xhtml" xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office"><head><!--[if gte mso 9]><xml><o:OfficeDocumentSettings><o:AllowPNG/><o:PixelsPerInch>96</o:PixelsPerInch></o:OfficeDocumentSettings></xml><![endif]--></head><body><div class="ydpbc0b9edyahoo-style-wrap" style="font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px;"><div style="font-size: 16px;"></div>
<div style="" dir="ltr" data-setdir="false"><font size="3">This issue makes me wonder, between these approaches:</font></div><div style="" dir="ltr" data-setdir="false"><font size="3">1. Resolve ALL legal ways of forming the hierarchy for RP and declare a </font><span style="font-size: medium;">tie among all possible victors.</span></div><div style="" dir="ltr" data-setdir="false"><span style="font-size: medium;"><span><font style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: 16px; background-color: inherit;">2. Same as #1 but with River</font><span style="color: rgb(0, 0, 0); font-family: Helvetica Neue, Helvetica, Arial, sans-serif; font-size: medium;">.</span></span><br></span></div><div style="" dir="ltr" data-setdir="false"><font size="3">3. Resolve Schulze, without handling a tie in the outcome.</font></div><div style="" dir="ltr" data-setdir="false"><font size="3"><br></font></div><div style="" dir="ltr" data-setdir="false"><font size="3">Do we expect differences in decisiveness? My hunch is yes... River admits fewer contests than RP so fewer ties can have an effect. For Schulze I'm not sure. It may be just an imaginary advantage, that the Schulze beatpath algorithm doesn't have to resolve tied contests mid-evaluation. On the other hand, maybe the defeat locking process (with the effect of dropping out some contests) has more potential to disrupt the outcome than exists in Schulze.</font></div><div style="" dir="ltr" data-setdir="false"><font size="3"><br></font></div><div style="" dir="ltr" data-setdir="false"><font size="3">Kevin</font></div><div style="" dir="ltr" data-setdir="false"><font size="3"><br></font></div><div style="font-size: 16px;"><br></div>
</div><div id="ydp1a75e810yahoo_quoted_1809411313" class="ydp1a75e810yahoo_quoted">
<div style="font-family: Helvetica Neue, Helvetica, Arial, sans-serif; color: rgb(38, 40, 42);">
<div style=""><font size="1">
Le vendredi 14 février 2020 à 08:46:44 UTC−6, Kristofer Munsterhjelm <km_elmet@t-online.de> a écrit :
</font></div>
<div style=""><font size="1"><br></font></div>
<div style=""><font size="1"><br></font></div>
<div style=""><div dir="ltr" style=""><font size="1">As far as I understand, Ranked Pairs and MAM need a tiebreaker to<br></font></div><div dir="ltr" style=""><font size="1">properly pass clone independence. The recommended tiebreaker is random<br></font></div><div dir="ltr" style=""><font size="1">ballot or random voter hierarchy. But is that tiebreaker summable? It<br></font></div><div dir="ltr" style=""><font size="1">seems you'd need to know the full ranking of the voter you choose for<br></font></div><div dir="ltr" style=""><font size="1">the random ballot, and you can't know what voter (or which voters)<br></font></div><div dir="ltr" style=""><font size="1">you're going to choose in advance.<br></font></div><div dir="ltr" style=""><font size="1"><br></font></div><div dir="ltr" style=""><font size="1">Is there a way to make random ballot or RVH summable?<br></font></div><div dir="ltr" style=""><font size="1"><br></font></div><div dir="ltr" style=""><font size="1">Even if you were to choose beforehand a lucky voter from each district<br></font></div><div dir="ltr" style=""><font size="1">and transmit that voter's preference ordering along with the district<br></font></div><div dir="ltr" style=""><font size="1">magnitude, you'd run into problems if a district's voter didn't rank<br></font></div><div dir="ltr" style=""><font size="1">every candidate.<br></font></div><div dir="ltr" style=""><font size="1"><br></font></div><div dir="ltr" style=""><font size="1">The two options to try to solve that would be to do random voter<br></font></div><div dir="ltr" style=""><font size="1">hierarchy with every district's predetermined lucky voter, or to do<br></font></div><div dir="ltr" style=""><font size="1">random voter hierarchy for each district so that the "composite lucky<br></font></div><div dir="ltr" style=""><font size="1">ballot" always fully specifies every candidate. But either choice would<br></font></div><div dir="ltr" style=""><font size="1">seem to alter the distribution. In the former case, you can't complete<br></font></div><div dir="ltr" style=""><font size="1">one district's voter's ballot with a ballot from the same district, and<br></font></div><div dir="ltr" style=""><font size="1">in the latter case, you can't complete one district's voter's ballot<br></font></div><div dir="ltr" style=""><font size="1">with a ballot from another district. Unrestricted random voter hierarchy<br></font></div><div dir="ltr" style=""><font size="1">can do both.<br></font></div><div dir="ltr" style=""><font size="1"><br></font></div><div dir="ltr" style=""><font size="1">Maybe this is not a problem and either of the completion strategies will<br></font></div><div dir="ltr" style=""><font size="1">work for clone independence purposes, but in that case, summable Ranked<br></font></div><div dir="ltr" style=""><font size="1">Pairs or MAM with multiple districts differs from summable Ranked Pairs<br></font></div><div dir="ltr" style=""><font size="1">or MAM in only one district. Or maybe I'm missing some easy way of<br></font></div><div dir="ltr" style=""><font size="1">making random ballot or RVH summable, in which case it'd be interesting<br></font></div><div dir="ltr" style=""><font size="1">to hear how to do so :-)<br></font></div><div dir="ltr" style=""><font size="1"><br></font></div><div dir="ltr" style=""><font size="1">-km<br></font></div><div dir="ltr" style=""><font size="1">----<br></font></div><div dir="ltr" style=""><font size="1">Election-Methods mailing list - see <a href="https://electorama.com/em " rel="nofollow" target="_blank" style="" class="enhancr_card_2044000534">https://electorama.com/em </a>for list info</font><div><br></div><div id="ydpf2996b8benhancr_card_2044000534" class="ydpf2996b8byahoo-link-enhancr-card ydpf2996b8byahoo-link-enhancr-not-allow-cover ydpf2996b8bymail-preserve-class ydpf2996b8bymail-preserve-style" style="max-width:400px;font-family:Helvetica Neue, Segoe UI, Helvetica, Arial, sans-serif" data-url="https://electorama.com/em" data-type="YENHANCER" data-size="MEDIUM" contenteditable="false"><a href="https://electorama.com/em" style="text-decoration:none !important;color:#000 !important" class="ydpf2996b8byahoo-enhancr-cardlink" rel="nofollow" target="_blank"><table border="0" class="ydpf2996b8bcard-wrapper ydpf2996b8byahoo-ignore-table" cellpadding="0" cellspacing="0" style="max-width:400px"><tbody><tr><td width="400"><table border="0" class="ydpf2996b8bcard ydpf2996b8byahoo-ignore-table" cellpadding="0" cellspacing="0" width="100%" style="max-width:400px;border-width:1px;border-style:solid;border-color:rgb(224, 228, 233);border-radius:2px"><tbody><tr><td><table border="0" class="ydpf2996b8bcard-info ydpf2996b8byahoo-ignore-table" cellpadding="0" cellspacing="0" style="background:#fff;position:relative;z-index:2;width:100%;max-width:400px;border-radius:0 0 2px 2px;border-top:1px solid rgb(224, 228, 233)"><tbody><tr><td style="background-color:#ffffff;padding:16px 0 16px 12px;vertical-align:top;border-radius:0 0 0 2px"></td><td style="vertical-align:middle;padding:12px 24px 16px 12px;width:99%;font-family:Helvetica Neue, Segoe UI, Helvetica, Arial, sans-serif;border-radius:0 0 2px 0"><h2 class="ydpf2996b8bcard-title" style="font-size: 14px; line-height: 19px; margin: 0px 0px 6px; font-family: Helvetica Neue, Segoe UI, Helvetica, Arial, sans-serif; color: rgb(38, 40, 42);">[EM] the election-methods mailing list</h2><p class="ydpf2996b8bcard-description" style="font-size: 12px; line-height: 16px; margin: 0px; color: rgb(151, 155, 167);"></p></td></tr></tbody></table></td></tr></tbody></table></td></tr></tbody></table></a></div><div><br></div><div><br></div><br></div></div>
</div>
</div></body></html>